Solve 6x^3y^-4/2x^-1y^3*x/2

$$\frac { 6 x ^ { 3 } y ^ { - 4 } } { 2 x ^ { - 1 } y ^ { 3 } } \times \frac { x } { 2 }$$

Evaluate

$$\frac{3x^{5}}{2y^{7}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3y^{-4}x^{3}}{\frac{1}{x}y^{3}}\times \frac{x}{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{3y^{-4}x^{4}}{y^{3}}\times \frac{x}{2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{3x^{4}}{y^{7}}\times \frac{x}{2}$$

Multiply \frac{3x^{4}}{y^{7}} times \frac{x}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3x^{4}x}{y^{7}\times 2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{3x^{5}}{y^{7}\times 2}$$

Differentiate w.r.t. x

$$\frac{15x^{4}}{2y^{7}}$$